(sorry for the novel-length post!)
Yes, he must be tested.
Men cannot be reliably tested for HPV and it can remain dormant. He can still pass it on to you, if the organism is present. Additionally, there are other diseases that can remain "hidden" for a long time.
Furthermore, his 4-year failure to be tested raises red flags; it is a sad but graphic reminder that you never can be certain that a cheater will become monogamous and therefore safe, sexually. This is why I recommend that there's no non-protected sex until there have been 2 years of tests, repeated at recommended intervals. (One test is insufficient; most doctors recommend repeat testing at intervals for 12-24 months because not all diseases manifest immediately; I err on the side of caution, as does my doctor, with 24 months of repeat testing.)
If, at the end of the 24 months or so, you are very confident NC has been established and you're well on the way to recovery with NO additional contact with ANY other affair partner, only then does it become safe(r), IMO, to have unprotected sex.
My husband LONG refused testing. He was not interested in sex with me. He wanted (1) a wife who provided creature comforts, and/or (2) a housekeeper with whom he had enough rapport that he could get the ego kibbles he wanted at home, which still getting sex outside the marriage.
In all honesty, he got #2 (no pun intended, but it's an apt descriptor, because it was really shitty for me) for a very, very long time.
But it was not sustainable for me. Not when there were additional d-days.
The 180 was a powerful tool for me, even when I was still stuck in the gotta-fix-this mode. (I spent far more time fighting for something in which he was utterly disinterested than a sane person would---but at the time, I was not sane.) It was a real epiphany to realize he wasn't changing.
You can't see the forest for the trees when you're spinning your wheels frantically to fix things. The mental quietude that the 180 creates is wonderful for creating enough emotional distance to gain more clarity. Even if you can't---as I couldn't!--apply all of its tenets all of the time, every bit that you master gives you strength.
Please, consider doing it. It will help you see the things you can control, as well as identify those you cannot. Instructions are located in the Healing Library (in the yellow box to the left), in the FAQs for BSs. It is #11.
Surrender. Surrender what you cannot control. I know that the word surrender has negative connotations; it conjures images of cowards waving white flags to escape consequences during wartime. But really, it requires tremendous strength---and the reward is tremendously freeing. If you cannot control something, there is no sense in trying. Surrender. Let go. Focus only on what you can control. (The concept of surrender was so life-changing for me that I have the word tattooed, now, inside my left wrist.)
Surrendering what you cannot control will give you freedom you don't even know is possible. It will free you from unnecessary pain. And as a mantra, it will remind you, with a single word, of the lessons held in the Serenity Prayer---which was also instrumental in my healing.
The Serenity Prayer was a really great anchor for me, in terms of guiding my emotions and actions. (My son, now almost 17, had it tattooed on his forearm; it was instrumental in pulling him out of the crushing depression his father's infidelity and abandonment triggered.)
It goes like this:
God grant me the serenity
to accept the things I cannot change;
the courage to change the things I can;
and the wisdom to know the difference.
Simple, right? Indeed, it is. And yet, it is so difficult. It is very hard to let go of the things we can't control---especially when swept away by an emotional tsunami. To survive this, you MUST let go, however, of the debris that does not serve you well. Then, you will have the strength to keep swimming, to stay afloat, to survive.
I am so sorry your husband has polluted your marriage. It is his responsibility to be tested. But it's NOT something you can control.
All you can control is your response to his failure/refusal to do so.
What will your consequences be? Will you require protected sex---but only AFTER the first round of tests comes back clean (and/or necessary treatment of treatable STDs is complete)? Will you re-evaluate your willingness to stay in the marriage?
Only you can draw your line in the stand.
But to do so, the distance afforded by the 180 can be really, really helpful. Even if you can't pull of a consistent, hard 180, every self-affirming action you do will make a difference in rebuilding yourself---which, remember, is all you can do---and help you survive this trauma, regardless of what your husband chooses to do.
Millions of hugs to you.